seulex.H

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License
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Class
    Foam::seulex

Description
    An extrapolation-algorithm, based on the linearly implicit Euler method
    with step size control and order selection.

    The implementation is based on the SEULEX algorithm in
    \verbatim
        "Solving Ordinary Differential Equations II: Stiff
         and Differential-Algebraic Problems, second edition",
        Hairer, E.,
        Nørsett, S.,
        Wanner, G.,
        Springer-Verlag, Berlin. 1996.
    \endverbatim

SourceFiles
    seulex.C

\*---------------------------------------------------------------------------*/

#ifndef seulex_H
#define seulex_H

#include "ODESolver.H"
#include "scalarMatrices.H"
#include "labelField.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

/*---------------------------------------------------------------------------*\
                           Class seulex Declaration
\*---------------------------------------------------------------------------*/

class seulex
:
    public ODESolver
{
    // Private data

        // Static constants

            static const label kMaxx_ = 12;
            static const label iMaxx_ = kMaxx_ + 1;

            static const scalar
                stepFactor1_, stepFactor2_, stepFactor3_,
                stepFactor4_, stepFactor5_,
                kFactor1_, kFactor2_;

        // Evaluated constants

            scalar jacRedo_;
            labelField nSeq_;
            scalarField cpu_;
            scalarSquareMatrix coeff_;

        // Temporary storage
        // held to avoid dynamic memory allocation between calls
        // and to transfer internal values between functions

            mutable scalar theta_;
            mutable label kTarg_;
            mutable scalarRectangularMatrix table_;

            mutable scalarField dfdx_;
            mutable scalarSquareMatrix dfdy_;
            mutable scalarSquareMatrix a_;
            mutable labelList pivotIndices_;

            // Fields space for "solve" function
            mutable scalarField dxOpt_, temp_;
            mutable scalarField y0_, ySequence_, scale_;

            // Fields used in "seul" function
            mutable scalarField dy_, yTemp_, dydx_;


    // Private Member Functions

        //- Computes the j-th line of the extrapolation table
        bool seul
        (
            const scalar x0,
            const scalarField& y0,
            const scalar dxTot,
            const label k,
            scalarField& y,
            const scalarField& scale
        ) const;

        //- Polynomial extrpolation
        void extrapolate
        (
            const label k,
            scalarRectangularMatrix& table,
            scalarField& y
        ) const;


public:

    //- Runtime type information
    TypeName("seulex");


    // Constructors

        //- Construct from ODE
        seulex(const ODESystem& ode, const dictionary& dict);


    // Member Functions

        //- Solve the ODE system and the update the state
        void solve
        (
            scalar& x,
            scalarField& y,
            stepState& step
        ) const;
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //